The coupling constants at finite temperature \(g_{\rho \Delta \Delta }(T)\) , \(g_{a_{1} \Delta \Delta }\) (T), and \(g_{\rho N \Delta }(T)\)  consists in numerical calculation of the integrals, and in numerically plotting their temperature dependencies by means of the Mathematical package. The author presents numerical results for the parameters \(N_{f}=2\) , \(F=87\)  MeV, \(N_{f}=3\) , \(F=100\)  MeV, \(N_{f}=4\) , \(F=130\)  MeV and flovour \(N_{f}=5\) , \(F=140\)  MeV. These sets of parameters were taken from [1]}
There are free parameters \(k\) , \(k_{1}\) , \(m_{q}\)  and \(\Sigma \)  in this work. The value of parameter \(k=383\)  MeV [2]} and parameter \(\overline{k}=-733\)  [1]}.
The parameters \(k_{1}\)  are fixed at the values \(k_{1}=-0.78\)  \( GeV^{3}\)  in the [4]}. The \(\Sigma =0.368^{3}\)  \(MeV^{3}\)  value and the \(m_{q}=0.0023\)  \(GeV\)  value of these parameters were found from the fitting of the \(\pi \)  meson mass [5]}.
Having an idea of the relative contributions of different flavors of hadrons, the author present results for the temperature dependencies of the various numbers separately.
